Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories

Masahito Hasegawa, Martin Hofmann, Gordon D. Plotkin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We show that the category FinVect k of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two different arrows in the free traced category there always exists a strong traced functor into FinVect k which distinguishes them. Therefore two arrows in the free traced category are the same if and only if they agree for all interpretations in FinVect k .
Original languageEnglish
Title of host publicationPillars of Computer Science
Subtitle of host publicationEssays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday
PublisherSpringer Berlin Heidelberg
Pages367-385
Number of pages19
Volume4800
ISBN (Electronic)978-3-540-78127-1
ISBN (Print)978-3-540-78126-4
DOIs
Publication statusPublished - 2008

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